Managing the intake of a certain nutrient can be an effective treatment for some inherited metabolic disorders. An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of the Phe to protein ratios. To be precise, we propose the multipliers 20 and 65 to obtain a minimum bound and a maximum bound for the Phe content from the protein content. The second approach is based on two simple lemmas which apply to sweets with gelatin. Specifically, we show that simple arithmetic operations can be used to determine an amount of sweets that is guaranteed to contain less than 20 mg Phe. The third approach is based on numerical optimization. We use the ingredient list and the Nutrition Facts Label to set up a set of inequalities which we solve numerically. The first step of our solution provides estimates for the ingredient amounts. This can be viewed as an approximate inverse recipe method. Although these mathematical methods are primarily motivated by the problem of estimating the Phe content, they can also be applied to estimating the content of other nutrient. In particular, they could be used to complete missing values in current food composition databases.
","abstract_html":"<p>Managing the intake of a certain nutrient can be an effective treatment for some inherited metabolic disorders. An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of the Phe to protein ratios. To be precise, we propose the multipliers 20 and 65 to obtain a minimum bound and a maximum bound for the Phe content from the protein content. The second approach is based on two simple lemmas which apply to sweets with gelatin. Specifically, we show that simple arithmetic operations can be used to determine an amount of sweets that is guaranteed to contain less than 20 mg Phe. The third approach is based on numerical optimization. We use the ingredient list and the Nutrition Facts Label to set up a set of inequalities which we solve numerically. The first step of our solution provides estimates for the ingredient amounts. This can be viewed as an approximate inverse recipe method. Although these mathematical methods are primarily motivated by the problem of estimating the Phe content, they can also be applied to estimating the content of other nutrient. In particular, they could be used to complete missing values in current food composition databases.</p>","abstract_has_math":false,"creators":["Kim, Jieun"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Mireille Boutin","Gregery Buzzard","Nung Kwan Aaron Yip","Carol J. Boushey"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-04-01T07:00:00Z","date_published":"2015-04-01T07:00:00Z","updated_at":"2026-07-24T03:53:28Z","subjects":["Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/488","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mireille Boutin","Gregery Buzzard","Nung Kwan Aaron Yip","Carol J. 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An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of the Phe to protein ratios. To be precise, we propose the multipliers 20 and 65 to obtain a minimum bound and a maximum bound for the Phe content from the protein content. The second approach is based on two simple lemmas which apply to sweets with gelatin. Specifically, we show that simple arithmetic operations can be used to determine an amount of sweets that is guaranteed to contain less than 20 mg Phe. The third approach is based on numerical optimization. We use the ingredient list and the Nutrition Facts Label to set up a set of inequalities which we solve numerically. The first step of our solution provides estimates for the ingredient amounts. This can be viewed as an approximate inverse recipe method. Although these mathematical methods are primarily motivated by the problem of estimating the Phe content, they can also be applied to estimating the content of other nutrient. In particular, they could be used to complete missing values in current food composition databases.
"]},{"key":"dc:title","label":"Title","values":["Mathematical approaches to food nutrient content estimation with a focus on phenylalanine"]}]}],"canonical_facts":{"dc:contributor":["Mireille Boutin","Gregery Buzzard","Nung Kwan Aaron Yip","Carol J. Boushey"],"dc:creator":["Kim, Jieun"],"dc:description.abstract":["Managing the intake of a certain nutrient can be an effective treatment for some inherited metabolic disorders. An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of the Phe to protein ratios. To be precise, we propose the multipliers 20 and 65 to obtain a minimum bound and a maximum bound for the Phe content from the protein content. The second approach is based on two simple lemmas which apply to sweets with gelatin. Specifically, we show that simple arithmetic operations can be used to determine an amount of sweets that is guaranteed to contain less than 20 mg Phe. The third approach is based on numerical optimization. We use the ingredient list and the Nutrition Facts Label to set up a set of inequalities which we solve numerically. The first step of our solution provides estimates for the ingredient amounts. This can be viewed as an approximate inverse recipe method. Although these mathematical methods are primarily motivated by the problem of estimating the Phe content, they can also be applied to estimating the content of other nutrient. In particular, they could be used to complete missing values in current food composition databases.
"],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/488"],"dc:subject":["Applied Mathematics"],"dc:title":["Mathematical approaches to food nutrient content estimation with a focus on phenylalanine"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:53:28Z"}